Obtaining cell complexes associated to four dimensional digital objects

Abstract

In this paper, we determine a cell complex representation of a 80–adjacent doxelbased 4-dimensional object. The homological information of this polyhedral cell complex can be employed to specify topological features and characteristics of a digital object. This homological information (for example, Euler characteristic, homological classification of cycles, homology generators, relations among them...) of a discrete object can be extracted from some specific boundary operators for each cell of an object (see [3]). The different (up to isometry) polyhedral cells are 400 configurations and their local boundary information can be suitably glued for determining the global boundary of an object and consequently, its corresponding homological information. This fact allows us to implement this technique using a look-up table for the different basic configurations and its corresponding boundary operators.